CHAPTER
1
Basic Electronics
Jack Ganssle
DC Circuits
“DC” means Direct Current, a fancy term for signals that don’t change. Flat lined, like a
corpse’s EEG or the output from a battery. Your PC’s power supply makes DC out of the
building’s AC (alternating current) mains. All digital circuits require DC power supplies.
Figure 1-1: A DC signal has a constant, unvarying amplitude.
Voltage and Current
We measure the quantity of electricity using voltage and amperage, but both arise from more
fundamental physics. Atoms that have a shortage or surplus of electrons are called ions. An
ion has a positive or negative charge. Two ions of opposite polarity (one plus, meaning it’s
missing electrons and the other negative, with one or more extra electrons) attract each other.
This attractive force is called the electromotive force, commonly known as EMF.
Charge is measured in coulombs, where one coulomb is 6.25 × 1018 electrons (for negative
charges) or protons for positive ones.
An ampere is one coulomb flowing past a point for one second. Voltage is the force between
two points for which one ampere of current will do one joule of work, a joule per second
being one watt.
But few electrical engineers remember these definitions and none actually use them.
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Chapter 1
Figure 1-2: A VOM, even an old-fashioned analog model like this $10
Radio Shack model, measures DC voltage as well or better than a scope.
An old but still apt analogy uses water flow through a pipe: current would be the amount of
water flowing through a pipe per unit time, while voltage is the pressure of the water.
The unit of current is the ampere (amp), though in computers an amp is an awful lot of
current. Most digital and analog circuits require much less. Here are the most common
nomenclatures:
Name
Abbreviation
# of amps
Where likely found
amp
A
1
Power supplies. Very high performance
processors may draw many tens of amps.
milliamp
mA
.001 amp
Logic circuits, processors (tens or hundreds of
mA), generic analog circuits.
microamp
µA
10-6 amp
Low power logic, low power analog, battery
backed RAM.
picoamp
pA
10-12 amp
Very sensitive analog inputs.
femtoamp
fA
10-15 amp
The cutting edge of low power analog
measurements.
Most embedded systems have a far less extreme range of voltages. Typical logic and
microprocessor power supplies range from a volt or two to five volts. Analog power supplies
rarely exceed plus and minus 15 volts. Some analog signals from sensors might go down to
the millivolt (.001 volt) range. Radio receivers can detect microvolt-level signals, but do this
using quite sophisticated noise-rejection techniques.
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Basic Electronics
Resistors
As electrons travel through wires, components, or accidentally through a poor soul’s body,
they encounter resistance, which is the tendency of the conductor to limit electron flow. A
vacuum is a perfect resistor: no current flows through it. Air’s pretty close, but since water is
a decent conductor, humidity does allow some electricity to flow in air.
Superconductors are the only materials with zero resistance, a feat achieved through the
magic of quantum mechanics at extremely low temperatures, on the order of that of liquid
nitrogen and colder. Everything else exhibits some resistance, even the very best wires. Feel
the power cord of your 1500 watt ceramic heater—it’s warm, indicating some power is lost in
the cord due to the wire’s resistance.
We measure resistance in ohms; the more ohms, the poorer the conductor. The Greek capital
omega (Ω) is the symbol denoting ohms.
Resistance, voltage, and amperage are all related by the most important of all formulas in
electrical engineering. Ohm’s Law states:
E=I×R
where E is voltage in volts, I is current in amps, and R is resistance in ohms. (EEs like to use
“E” for volts as it indicates electromotive force).
What does this mean in practice? Feed one amp of current through a one-ohm load and there
will be one volt developed across the load. Double the voltage and, if resistance stays the
same, the current doubles.
Though all electronic components have resistance, a resistor is a device specifically made to
reduce conductivity. We use them everywhere. The volume control on a stereo (at least, the
non-digital ones) is a resistor whose value changes as you rotate the knob; more resistance
reduces the signal and hence the speaker output.
Figure 1-3: The squiggly thing on the left is the standard symbol used
by engineers to denote a resistor on their schematics. On the right is
the symbol used by engineers in the United Kingdom. As Churchill said,
we are two peoples divided by a common language.
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Chapter 1
Name
Abbreviation
ohms
Where likely found
milliohm
mΩ
.001 ohm
Resistance of wires and other good
conductors.
ohm
Ω
1 ohm
Power supplies may have big dropping
resistors in the few to tens of ohms range.
hundreds
of ohms
In embedded systems it’s common to find
resistors in the few hundred ohm range
used to terminate high speed signals.
kiloohm
k Ω or just k
1000 ohms
Resistors from a half-k to a hundred or
more k are found all over every sort of
electronic device. “Pullups” are typically
a few k to tens of k.
megaohm
MΩ
106 ohms
Low signal-level analog circuits.
108++ ohms
Geiger counters and other extremely
sensitive apps; rarely seen as resistors of
this size are close to the resistance of air.
hundreds
of M Ω
Table 1-1: Range of values for real-world resistors.
What happens when you connect resistors together? For resistors in series, the total effective
resistance is the sum of the values:
Reff = R1 + R2
For two resistors in parallel, the effective resistance is:
Reff =
(Thus, two identical resistors in parallel are effectively half the resistance of either of them:
two 1ks is 500 ohms. Now add a third: that’s essentially a 500-ohm resistor in parallel with a
1k, for an effective total of 333 ohms).
The general formula for more than two resistors in parallel is:
Reff =
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Basic Electronics
Figure 1-4: The three series resistors on the left are
equivalent to a single 3000-ohm part. The three
paralleled on the right work out to one 333-ohm device.
Manufacturers use color codes to denote the value of a particular resistor. While at first this
may seem unnecessarily arcane, in practice it makes quite a bit of sense. Regardless of
orientation, no matter how it is installed on a circuit board, the part’s color bands are always
visible.
Figure 1-5: This black and white photo masks the resistor’s color bands.
However, we read them from left to right, the first two designating
the integer part of the value, the third band giving the multiplier.
A fourth gold (5%) or silver (10%) band indicates the part’s tolerance.
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Chapter 1
Color Band
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold (3rd band)
Silver (3rd band)
Value
Multiplier
0
1
2
3
4
5
6
7
8
9
1
10
100
1000
10,000
100,000
1,000,000
not used
not used
not used
÷10
÷100
Table 1-2: The resistor color code. Various mnemonic devices designed to help one
remember these are no longer politically correct; one acceptable but less memorable
alternative is Big Brown Rabbits Often Yield Great Big Vocal Groans When Gingerly Slapped.
The first two bands, reading from the left, give the integer part of the resistor’s value. The
third is the multiplier. Read the first two band’s numerical values and multiply by the scale
designated by the third band. For instance: brown black red = 1 (brown) 0 (black) times 100
(red), or 1000 ohms, more commonly referred to as 1k. The following table has more
examples.
First
band
Second
band
Third
band
Calculation
Value
(ohms)
Commonly
called
brown
red
orange
green
green
red
brown
blue
red
red
orange
blue
blue
red
black
gray
orange
red
yellow
red
green
black
gold
red
12 x 1000
22 x 100
33 x 10,000
56 x 100
56 x 100,000
22 x 1
10 ÷10
68 x 100
12,000
2,200
330,000
5,600
5,600,000
22
1
6,800
12k
2.2k
330k
5.6k
5.6M
22
1
6.8k
Table 1-3: Examples showing how to read color bands and compute resistance.
Resistors come in standard values. Novice designers specify parts that do not exist; the
experienced engineer knows that, for instance, there’s no such thing as a 1.9k resistor.
Engineering is a very practical art; one important trait of the good designer is using standard
and easily available parts.
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Basic Electronics
Circuits
Electricity always flows in a loop. A battery left disconnected discharges only very slowly
since there’s no loop, no connection of any sort (other than the non-zero resistance of humid
air) between the two terminals. To make a lamp light, connect one lead to each battery
terminal; electrons can now run in a loop from the battery’s negative terminal, through the
lamp, and back into the battery.
There are only two types of circuits: series and parallel. All real designs use combinations of
these. A series circuit connects loads in a circular string; current flows around through each
load in sequence. In a series circuit the current is the same in every load.
Figure 1-6: In a series circuit the electrons flow through one load
and then into another. The current in each resistor is the same;
the voltage dropped across each depends on the resistor’s value.
It’s easy to calculate any parameter of a series circuit. In the diagram above a 12-volt battery
powers two series resistors. Ohm’s Law tells us that the current flowing through the circuit is
the voltage (12 in this case) divided by the resistance (the sum of the two resistors, or 12k).
Total current is thus:
I = V ÷ R = (12 volts) ÷ (2000 + 10,000 ohms) = 12 ÷ 12000 = 0.001 amp = 1 mA
(remember that mA is the abbreviation for milliamps).
So what’s the voltage across either of the resistors? In a series circuit the current is identical
in all loads, but the voltage developed across each load is a function of the load’s resistance
and the current. Again, Ohm’s Law holds the secret. The voltage across R1 is the current in
the resistor times its resistance, or:
VR1 = IR1 = 0.001 amps × 2000 ohms = 2 volts
Since the battery places 12 volts across the entire resistor string, the voltage dropped on R2
must be 12 – 2, or 10 volts. Don’t believe that? Use Mr. Ohm’s wonderful equation on R2
to find:
VR2 = IR2 = 0.001 amps × 10,000 ohms = 10 volts
It’s easy to extend this to any number of parts wired in series.
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Chapter 1
Parallel circuits have components wired so both pins connect. Current flows through both
parts, though the amount of current depends on the resistance of each leg of the circuit. The
voltage, though, on each component is identical.
Figure 1-7: R1 and R2 are in parallel, both driven by the 12 volt battery.
We can compute the current in each leg much as we did for the series circuit. In the case
above the battery applies 12 volts to both resistors. The current through R1 is:
IR1 = 12 volts ÷ 2,000 ohms = 12 ÷ 2000 = 0.006 amps = 6 mA
Through R2:
IR2 = 12 volts ÷ 10,000 ohms = 0.0012 amps = 1.2 mA
Real circuits are usually a combination of series and parallel elements. Even in these more
complex, more realistic cases it’s still very simple to compute anything one wants to know.
Figure 1-8: A series/parallel circuit.
Let’s analyze the circuit shown above. There’s only one trick: cleverly combine complicated
elements into simpler ones. Let’s start by figuring the current flowing out of the battery. It’s
much too hard to do this calculation till we remember that two resistors in parallel look like a
single resistor with a lower value.
Start by figuring the current flowing out of the battery and through R1. We can turn this into
a series circuit (in which the current flowing is the same through all of the components) by
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Basic Electronics
replacing R3 and R2 by a single resistor with the same effective value as these two paralleled
components. That’s:
So the circuit is identical to one with two series resistors: R1, still 1k, and REFF at 1474 ohms.
Ohm’s Law gives the current flowing out of the battery and through these two resistors:
Ohm’s Law remains the font of all wisdom in basic circuit analysis, and readily tells us the
voltage dropped across R1:
Clearly, since the battery provides 10 volts, the voltage across the paralleled pair R2 and R3
is 6 volts.
Power
Power is the product of voltage and current and is expressed in watts. One watt is one volt
times one amp. A milliwatt is a thousandth of a watt; a microwatt a millionth.
You can think of power as the total amount of electricity present. A thousand volts sounds
like a lot of electricity, but if there’s only a microamp available that’s a paltry milliwatt—not
much power at all.
Power is also current2 times resistance:
P = I2 × R
Electronic components like resistors and ICs consume a certain amount of volts and amps.
An IC doesn’t move, make noise, or otherwise release energy (other than exerting a minimal
amount of energy in sending signals to other connected devices), so almost all of the energy
consumed gets converted to heat. All components have maximum power dissipation ratings;
exceed these at your peril.
If a part feels warm it’s dissipating a reasonable fraction of a watt. If it’s hot but you can keep
your finger on it, then it’s probably operating within specs, though many analog components
want to run cooler. If you pull back, not burned but the heat is too much for your finger, then
in most cases (be wary of the wimp factor; some people are more heat sensitive than others)
the device is too hot and either needs external cooling (heat sink, fan, etc.), has failed, or your
circuit exceeds heat parameters. A burn or near burn, or discoloration of the device, means
there’s trouble brewing in all but exceptional conditions (e.g., high energy parts like power
resistors).
A PC’s processor has so many transistors, each losing a bit of heat, that the entire part might
consume and eliminate 100+ watts. That’s far more than the power required to destroy the
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Chapter 1
chip. Designers expend a huge effort in building heat sinks and fans to transfer the energy in
the part to the air.
The role of heat sinks and fans is to remove the heat from the circuits and dump it into the air
before the devices burn up. The fact that a part dissipates a lot of energy and wants to run hot
is not bad as long as proper thermal design removes the energy from the device before it
exceeds its max temp rating.
Figure 1-9: This 10-ohm resistor, with 12 volts applied, draws 833 mA. P = I2R, so it’s
sucking about 7 watts. Unfortunately, this particular part is rated for ¼ watt max, so is on
fire. Few recent college grads have a visceral feel for current, power and heat, so this demo
makes their eyes go like saucers.
AC Circuits
AC is short for alternating current, which is any signal that’s not DC. AC signals vary with
time. The mains in your house supply AC electricity in the shape of a sine wave: the voltage
varies from a large negative to a large positive voltage 60 times per second (in the USA and
Japan) or 50 times (in most of the rest of the world).
AC signals can be either periodic, which means they endlessly and boringly repeat forever, or
aperiodic, the opposite. Static from your FM radio is largely aperiodic as it’s quite random.
The bit stream on any address or data line from a micro is mostly aperiodic, at least over
short times, as it’s a complex changing pattern driven by the software.
The rate at which a periodic AC signal varies is called its frequency, which is measured in
hertz (Hz for short). One Hz means the waveform repeats once per second. 1000 Hz is a kHz
(kilohertz), a million Hz is the famous MHz by which so many microprocessor clock rates
are defined, and a billion Hz is a GHz.
The reciprocal of Hz is period. That is, where the frequency in hertz defines the signal’s
repetition rate, the period is the time it takes for the signal to go through a cycle.
Mathematically:
Period in seconds = 1 ÷ frequency in Hz
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Basic Electronics
Thus, a processor running at 1 GHz has a clock period of 1 nanosecond—one billionth of a
second. No kidding. In that brief flash of time even light goes but a bare foot. Though your
1.8 GHz PC may seem slow loading Word®, it’s cranking instructions at a mind-boggling rate.
Wavelength relates a signal’s period—and thus its frequency—to a physical “size.” It’s the
distance between repeating elements, and is given by:
Wavelength in meters =
where c is the speed of light.
An FM radio station at about 100 MHz has a wavelength of 3 meters. AM signals, on the
other hand, are around 1 MHz so each sine wave is 300 meters long. A 2.4-GHz cordless
phone runs at a wavelength a bit over 10 cm.
As the frequency of an AC signal increases, things get weird. The basic ideas of DC circuits
still hold, but need to be extended considerably. Just as relativity builds on Newtonian
mechanics to describe fast-moving systems, electronics needs new concepts to properly
describe fast AC circuits.
Resistance, in particular, is really a subset of the real nature of electronic circuits. It turns out
there are three basic kinds of resistive components; each behaves somewhat differently.
We’ve already looked at resistors; the other two components are capacitors and inductors.
Both of these parts exhibit a kind of resistance that varies depending on the frequency of the
applied signal; the amount of this “AC resistance” is called reactance.
Capacitors
A capacitor, colloquially called the “cap,” is essentially two metal plates separated from each
other by a thin insulating material. This insulation, of course, means that a DC signal cannot
flow through the cap. It’s like an open circuit.
But in the AC world strange things happen. It turns out that AC signals can make it across the
gap between the two plates; as the frequency increases the effective resistance of this gap
decreases. This resistive effect is called reactance; for a capacitor it’s termed capacitive
reactance. There’s a formula for everything in electronics; for capacitive reactance it’s:
where:
Xc = capacitive reactance
f = frequency in Hz
c = capacitance in farads
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Chapter 1
Figure 1-10: Capacitive reactance of a 0.1 µF cap (top) and a 0.5 µF cap (bottom curve).
The vertical axis is reactance in ohms. See how larger caps have lower reactances,
and as the frequency increases reactance decreases. In other words, a bigger cap
passes AC better than a smaller one, and at higher frequencies all caps pass more
AC current. Not shown: at 0 Hz (DC), reactance of all caps is essentially infinite.
Capacitors thus pass only changing signals. The current flowing through a cap is:
(If your calculus is rusty or nonexistent, this simply means that the current flow is proportional to the change in voltage over time.)
In other words, the faster the signal changes, the more current flows.
Name
Abbreviation
farads
Where likely found
picofarad
pF
10-12 farad
microfarad
µF
10-6 farad
farad
F
1 farad
Padding caps on microprocessor crystals,
oscillators, analog feedback loops.
Decoupling caps on chips are about .01
to .1µF. Low freq decoupling runs about
10µF, big power supply caps might be
1000µF.
One farad is a huge capacitor and
generally does not exist. A few vendors
sell “supercaps” that have values up to a
few farads but these are unusual. Sometimes used to supply backup power to
RAMs when the system is turned off.
Table 1-4: Range of values for real-world capacitors.
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Basic Electronics
In real life there’s no such thing as a perfect capacitor. All leak a certain amount of DC and
exhibit other more complex behavior. For that reason, there’s quite a range of different types
of parts.
In most embedded systems you’ll see one of two types of capacitors. The first are the polarized ones, devices which have a plus and a minus terminal. Connect one backwards and the
part will likely explode!
Polarized devices have large capacitance values: tens to thousands of microfarads. They’re
most often used in power supplies to remove the AC component from filtered signals. Consider the equation of capacitive reactance: large cap values pass lower frequency signals
efficiently. Typical construction today is from a material called “tantalum”; seasoned EEs
often call these devices “tantalums.” You’ll see tantalum caps on PC boards to provide a bit
of bulk storage of the power supply.
Smaller caps are made from a variety of materials. These have values from a few picofarads
to a fraction of a microfarad. Often used to “decouple” the power supply on a PCB (i.e., to
short high frequency switching from power to ground, so the logic signals don’t get coupled
into the power supply). Most PCBs have dozens or hundreds of these parts scattered around.
Figure 1-11: Schematic symbols for capacitors. The one on the left is a
generic, generally low-valued (under 1 µF) part. On the right the plus sign
shows the cap is polarized. Installed backwards, it’s likely to explode.
We can wire capacitors in series and in parallel; compute the total effective capacitance using
the rules opposite those for resistors. So, for two caps in parallel sum their values to get the
effective capacitance. In a series configuration the total effective capacitance is:
Note that this rule is for figuring the total capacitance of the circuit, and not for computing
the total reactance. More on that shortly.
One useful characteristic of a capacitor is that it can store a charge. Connect one to a battery
or power supply and it will store that voltage. Remove the battery and (for a perfect, lossless
17
Chapter 1
part) the capacitor will still hold that voltage. Real parts leak a bit; ones rated at under 1 µF
or so discharge rapidly. Larger parts store the charge longer.
Interesting things happen when wiring a cap and a resistor in series. The resistor limits
current to the capacitor, causing it to charge slowly. Suppose the circuit shown in the following diagram is dead, no voltage at all applied. Now turn on the switch. Though we’ve applied
a DC signal, the sudden transition from 0 to 5 volts is AC.
Current flows due to the
rule; dV is the sudden edge from flipping the switch.
But the input goes from an AC-edge to steady-state DC, so current stops flowing pretty
quickly. How fast? That’s defined by the circuit’s time constant.
Figure 1-12: Close the switch and the voltage applied to the RC circuit
looks like the top curve. The lower graph shows how the capacitor’s voltage
builds slowly with time, headed asymptotically towards the upper curve.
A resistor and capacitor in series is colloquially called an RC circuit. The graph shows how
the voltage across the capacitor increases over time. The time constant of any circuit is pretty
well approximated by:
t = RC
for R in ohms, C in farads, and t in seconds.
This formula tells us that after RC seconds the capacitor will be charged to 63.2% of the
battery’s voltage. After another RC seconds another 63.2%, for a total now of 86.5%.
Analog circuits use a lot of RC circuits; in a microprocessor it’s still common to see them
controlling the CPU’s reset input. Apply power to the system and all of the logic comes up,
but the RC’s time constant keeps reset asserted low for a while, giving the processor time to
initialize itself.
The most common use of capacitors in the digital portion of an embedded system is to
decouple the logic chips’ power pins. A medium value part (0.01 to 0.1 µF) is tied between
power and ground very close to the power leads on nearly every digital chip. The goal is to
keep power supplied to the chips as clean as possible—close to a perfect DC signal.
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Basic Electronics
Why would this be an issue? After all, the system’s power supply provides a nearly perfect
DC level. It turns out that as a fast logic chip switches between zero and one it can draw
immense amounts of power for a short, sub-nanosecond, time. The power supply cannot
respond quickly enough to regulate that, and since there’s some resistance and reactance
between the supply and the chip’s pins, what the supply provides and what the chip sees is
somewhat different. The decoupling capacitor shorts this very high frequency (i.e., short
transient) signal on Vcc to ground. It also provides a tiny bit of localized power storage that
helps overcome the instantaneous voltage drop between the power supply and the chip.
Most designs also include a few tantalum bulk storage devices scattered around the PC board,
also connected between Vcc and ground. Typically these are 10 to 50 µf each. They are even
more effective bulk storage parts to help minimize the voltage drop chips would otherwise see.
You’ll often see very small caps (on the order of 20 pF) connected to microprocessor drive
crystals. These help the device oscillate reliably.
Analog circuits make many wonderful and complex uses of caps. It’s easy to build integrators
and differentiators from these parts, as well as analog hold circuits that memorize a signal for
a short period of time. Common values in these sorts of applications range from 100 pF to
fractions of a microfarad.
Inductors
An inductor is, in a sense, the opposite of a capacitor. Caps block DC but offer diminishing
resistance (really, reactance) to AC signals as the frequency increases. An inductor, on the
other hand, passes DC with zero resistance (for an idealized part), but the resistance (reactance) increases proportionately to the frequency.
Physically an inductor is a coil of wire, and is often referred to as a coil. A simple straight wire
exhibits essentially no inductance. Wrap a wire in a loop and it’s less friendly to AC signals.
Add more loops, or make them smaller, or put a bit of ferrous metal in the loop, and inductance
increases. Electromagnets are inductors, as is the field winding in an alternator or motor.
An iron core inductor is wound around a slug of metal, which increases the device’s inductance substantially.
Inductance is measured in henries (H). Inductive reactance is the tendency of an inductor to
block AC, and is given by:
where:
XL = Inductive reactance
f = frequency in Hz
L = inductance in henries
Clearly, as the frequency goes to zero (DC), reactance does as well.
19
Chapter 1
Figure 1-13: Schematic symbols of two inductors. The one on
the left is an “air core”; that on the right an “iron core.”
Inductors follow the resistor rules for parallel and series combinations: add the value (in
henries) when in series, and use the division rule when in parallel.
Inductors are much less common in embedded systems than are capacitors, yet they are
occasionally important. The most common use is in switching power supplies. Many
datacomm circuits use small inductors (generally millihenries) to match the network being
driven.
Power supplies usually have a transformer which reduces the AC mains (from the wall) to a
lower voltage more appropriate for embedded systems.
Figure 1-14: The schematic symbol for a transformer.
Transformers are two inductors wrapped around each other, with an iron core. The input AC
generates a changing magnetic field, which induces a voltage in the output (“secondary”)
inductor.
If both inductors have the same number of wire loops, the output voltage is the same as the
input. If the secondary has fewer loops, the voltage is less.
Sometimes signals, especially those flowing off a PC board, will have a ferrite bead wrapped
around the wire. These beads are small cylinders (a few mm long) made of a ferromagnetic
material. Like all inductors they help block AC so are used to minimize noise of signal wires.
Active Devices
Resistors, capacitors and inductors are the basic passive components, passive meaning
“dumb.” The parts can’t amplify or dramatically change applied signals. By contrast, active
parts can clip, amplify, distort and otherwise change an applied signal.
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Basic Electronics
The earliest active parts were vacuum tubes, called “valves” in the UK.
Figure 1-15: On the left, a schematic of a dual triode
vacuum tube. The part itself is shown on the right.
Consider the schematic above, which is a single tube that contains two identical active
elements, each called a “triode,” as each has three terminals. Tubes are easy to understand;
let’s see how one works.
A filament heats the cathode, which emits a stream of electrons. They flow through the grid, a
wire mesh, and are attracted to the plate. Electrons are negatively charged, so applying a very
small amount of positive voltage to the grid greatly reduces their flow. This is the basis of
amplification: a small control signal greatly affects the device’s output.
Of course, in the real world tubes are almost unheard of today. When Bardeen, Brattain, and
Shockley invented the transistor in 1947 they started a revolution that continues today. Tubes
are power hogs, bulky and fragile. Transistors—also three-terminal devices that amplify—
seem to have no lower limit of size and can run on picowatts.
Figure 1-16: The schematic diagram of a
bipolar NPN transistor with labeled terminals.
A transistor is made from a single crystal, normally of silicon, into which impurities are
doped to change the nature of the material. The tube description showed how it’s a voltage
controlled device; bipolar transistors are current controlled.
Writers love to describe transistor operation by analogy to water flow, or to the movement of
holes and carriers within the silicon crystal. These are at best poor attempts to describe the
quantum mechanics involved. Suffice to say that, in the picture above, feeding current into
the base allows current to flow between the collector and emitter.
21
Chapter 1
Figure 1-17: A very simple amplifier.
And that’s about all you need to know to get a sense of how a transistor amplifier works. The
circuit above is a trivialized example of one. A microphone—which has a tiny output—drives
current into the base of the transistor, which amplifies the signal, causing the lamp to fluctuate in rhythm with the speaker’s voice.
A real amplifier might have many cascaded stages, each using a transistor to get a bit of
amplification. A radio, for instance, might have to increase the antenna’s signal by many
millions before it gets to the speakers.
Figure 1-18: A NOR gate circuit.
22
Basic Electronics
Transistors are also switches, the basic element of digital circuits. The previous circuit is a
simplified—but totally practical—NOR gate. When both inputs are zero, both transistors are
off. No current flows from their collectors to emitters, so the output is 5 volts (as supplied by
the resistor).
If either input goes to a high level, the associated transistor turns on. This causes a conduction path through the transistor, pulling “out” low. In other words, any input going to a one
gives an output of zero. The truth table below illustrates the circuit’s behavior.
in1
in2
out
0
0
1
1
0
1
0
1
1
0
0
0
It’s equally easy to implement any logic function.
The circuit we just analyzed would work; in the 1960s all “RTL” integrated circuits used
exactly this design. But the gain of this approach is very low. If the input dawdles between a
zero and a one, so will the output. Modern logic circuits use very high amplification factors,
so the output is either a legal zero or one, not some in-between state, no matter what input is
applied.
The silicon is a conductor, but a rather lousy one compared to a copper wire. The resistance
of the device between the collector and the emitter changes as a function of the input voltage;
for this reason active silicon components are called semiconductors.
Transistors come in many flavors; the one we just looked at is a bipolar part, characterized by
high power consumption but (typically) high speeds. Modern ICs are constructed from
MOSFET—Metal Oxide Semiconductor Field Effect Transistor—devices, or variants
thereof. A mouthful? You bet. Most folks call these transistors FETs for short.
Figure 1-19: The schematic diagram of a MOSFET.
A FET is a strange and wonderful beast. The gate is insulated by a layer of oxide from a
silicon channel running between the drain and source. No current flows from the gate to the
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Chapter 1
silicon channel. Yet putting a bias voltage (like a tube, a FET is a voltage device) on the gate
creates an electrostatic field that reduces current flow between the other two terminals. Again,
no current flows from the gate. And when turned on, the source-drain resistance is much
lower than in a bipolar transistor. This means the part dissipates little power, a critical concern when putting millions of these transistors on a single IC.
Figure 1-20: The schematic symbol for a diode.
A diode is a two-terminal semiconductor that passes current in one direction only. In the
picture above, a positive voltage will flow from the left to the right, but not in the reverse
direction. Seems a little thing, but it’s incredibly useful. The following circuit implements an
OR gate without a transistor:
Figure 1-21: A diode OR circuit.
If both inputs are logic one, the output is a one (pulled up to +5 by the resistor). Any input
going low will drag the output low as well. Yet the diodes insure that a low-going input
doesn’t drag the other input down.
Putting it Together—a Power Supply
A power supply is a simple yet common circuit that uses many of the components we’ve
discussed. The input is 110 volts AC (or 220 volts in Europe, 100 in Japan, 240 in the UK).
Output might be 5 volts DC for logic circuits. How do we get from high voltage AC input to
5 volts DC?
The first step is to convert the AC mains to a lower voltage AC, as follows:
24
Basic Electronics
Now let’s turn that lower voltage AC into DC. A diode does the trick nicely:
The AC mains are a sine wave, of course. Since the diode conducts in one direction only, its
output looks like:
This isn’t DC… but the diode has removed all of the negative-going parts of the waveform.
But we’ve thrown away half the signal; it’s wasted. A better circuit uses four diodes arranged
in a bridge configuration as follows:
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Chapter 1
The bridge configuration ensures that two diodes conduct on each half of the AC input, as
shown above. It’s more efficient, and has the added benefit of doubling the apparent frequency, which will be important when figuring out how to turn this moving signal into a
DC level.
The average of this signal is clearly a positive voltage, if only we had a way to create an
average value. Turns out that a capacitor does just that:
A huge value capacitor filters best—typical values are in the thousands of microfarads.
The output is a pretty decent DC wave, but we’re not done yet. The load—the device this
circuit will power—will draw varying amounts of current. The diodes and transformer both
have resistance. If the load increases, current flow goes up, so the drop across the parts will
increase (Ohm’s Law tells us E = IR, and as I goes up, so does E). Logic circuits are very
sensitive to fluctuations in their power, so some form of regulation is needed.
A regulator takes varying DC in, and produces a constant DC level out. For example:
The odd-looking part in the middle is a zener diode. The voltage drop across the zener is
always constant, so if, for example, this is a 3-volt part, the intersection of the diode and the
resistor will always be 3 volts.
The regulator’s operation is straightforward. The zener’s output is a constant voltage. The
triangle is a bit of magic—an error amplifier circuit—that compares the zener’s constant
voltage to the output of the power supply (at the node formed by the two resistors). If the
26
Basic Electronics
output voltage goes up, the error amplifier applies less bias to the base of the transistor,
making it conduct less… and lowering the supply’s output. The transistor is key to the
circuit; it’s sort of like a variable resistor controlled by the error amp.
If, say, 20 volts of unregulated DC goes into the transistor from the bridge and capacitor, and
the supply delivers 5 volts to the logic, there’s 15 volts dropped across the transistor. If the
supply provides even just two amps of current, that’s 30 watts (15 volts times two amps)
dissipated by that semiconductor—a lot of heat! Careful heatsinking will keep the device
from burning up.
The Scope
Figure 1-22: A sea of knobs. Don’t be intimidated. There’s a logical grouping to these.
Master them and wow your friends and family. Photo courtesy of Tektronix, Inc.
The oscilloscope (colloquially known as the “scope”) is the most basic tool used for troubleshooting and understanding electronic circuits. Without some understanding of this most
critical of all tools, you’ll be like a blind person trying to understand color.
The scope has only one function: it displays a graph of the signal or signals you’re probing.
The horizontal axis is usually time; the vertical is amplitude, a fancy electronics term for
voltage.
27
Chapter 1
Controls
Figure 1-23: Typical oscilloscope front panel. Picture courtesy Tektronix, Inc.
In the above picture note first the two groups of controls labeled “vertical input 1” and
“vertical input 2.” This is a two-channel scope, by far the most common kind, which allows
you to sample and display two different signals at the same time.
The vertical controls are simple. “Position” allows you to move the graphed signal up and
down on the screen to the most convenient viewing position. When looking at two signals it
allows you to separate them, so they don’t overlap confusingly.
“Volts/div” is short for volts-per-division. You’ll note the screen is a matrix of 1 cm by 1 cm
boxes; each is a “division.” If the “volts/div” control is set to 2, then a two volt signal extends
over a single division. A five-volt signal will use 2.5 divisions. Set this control so the signal
is easy to see. A reasonable setting for TTL (5 volt) logic is 2 volts/div.
Figure 1-24: The signal is an AC waveform riding on top of a constant DC signal. On the left
we’re observing it with the scope set to DC coupling; note how the AC component is moved
up by the amount of DC (in other words, the total signal is the DC component + the AC).
On the right we’ve changed the coupling control to “AC”; the DC bias is removed and the
AC component of the signal rides in the middle of the screen.
28
Basic Electronics
The “coupling” control selects “DC”—which means what you see is what you get. That is,
the signal goes unmolested into the scope. “AC” feeds the input through a capacitor; since
caps cannot pass DC signals, this essentially subtracts DC bias.
The “mode” control lets us look at the signal on either channel, or both simultaneously.
Now check out the horizontal controls. These handle the scope’s “time base,” so called
because the horizontal axis is always the time axis.
The “position” control moves the trace left and right, analogously to the vertical channel’s
knob of the same name.
“Time/div” sets the horizontal axis’ scale. If set to 20 nsec/div, for example, each cm on the
screen corresponds to 20 nsec of time. Figure 1-25 shows the same signal displayed using
two different time base settings; it’s more compressed in the left picture simply because at
2000µsec/div more pulses occur in the one cm division mark.
Figure 1-25: The left picture shows a signal with the time base set to 2000 µsec/division;
the right is the same signal but now we’re sweeping at 200 µsec/division. Though the
data is unchanged, the signal looks compressed. Also note that the 5-volt signal extends
over 2.5 vertical boxes, since the gain is set to 2 volts/div. The first rule of scoping is
to know the horizontal and vertical settings.
The last bank of knobs—those labeled “trigger”—are perhaps the most important of all.
Though you see a line on the screen, it’s formed by a dot swept across from left to right,
repeatedly, at a very high speed. How fast? The dot moves at the speed you’ve set in the time/
div knob. At 1 sec/div the dot takes 10 seconds to traverse the normal 10 cm-wide scope
screen. More usual speeds for digital work are in the few microseconds to nanosecond range,
so the dot moves faster than any eye can track.
Most of the signals we examine are more or less repetitive: it’s pretty much the same old
waveform over and over again. The trigger controls tell the scope when to start sweeping the
dot across the screen. The alternative—if the dot started on the left side at a random time—
would result in a very quickly scrolling screen, which no one could follow.
Twiddling the “trigger level” control sets the voltage at which the dot starts its inexorable
left-to-right sweep. Set it to 6 volts and the normal 5-volt logic signal will never get high
29
Chapter 1
enough that the dot starts. The screen stays blank. Crank it to zero and the dot runs continuously, unsynchronized to the signal, creating a scrambled mess on the scope screen.
Set trigger-level to 2 volts or so, and as the digital signal traverses from 0 to 5 volts the dot
starts scanning, synchronizing now to the signal.
It’s most dramatic to learn this control when sampling a sine wave. As you twirl the knob
clockwise (from a low trigger voltage to a higher one) the displayed sine wave shifts to the
left. That is, the scan starts later and later since the triggering circuit waits for an everincreasing signal voltage before starting.
“Trigger Menu” calls up a number of trigger selection criterion. Select “trigger on positive
edge” and the scope starts sweeping when the signal goes from a low level through the
trigger voltage set with the “Trigger Level” knob. “Trigger on negative edge” starts the sweep
when the signal falls from a high level through the level.
Every scope today has more features than normal humans can possibly remember, let alone
use. Various on-screen menus let you do math on the inputs (add them, etc), store signals that
occur once, and much, much more. The instrument is just like a new PC application. Sure,
it’s nice to read the manual, but don’t be afraid to punch a lot of buttons and see what happens. Most functions are pretty intuitive.
Probes
Figure 1-26: Always connect the probe’s ground lead to the system.
A “probe” connects the scope to your system. Experienced engineers’ fingers are permanently
bent a bit, warped from too many years holding the scope probe in hand while working on
circuit boards. Though electrically the probe is just a wire, in fact there’s a bit of electronics
magic inside to propagate signals without distortion from your target system to the scope.
So too for any piece of test equipment. The tip of the scope probe is but one of the two
connections required between the scope and your target system. A return path is needed, a
ground. If there’s no ground connection the screen will be nutso, s swirling mass of meaningless scrolling waveforms.
30
Basic Electronics
Yet often we’ll see engineers probing nonchalantly without an apparent ground connection.
Oddly, the waves look fine on the scope. What gives? Where’s the return path?
It’s in the lab wall. Most electric cords, including the one to the scope and possibly to your
target system, have three wires. One is ground. It’s pretty common to find the target grounded
to the scope via this third wire, going through the wall outlets. Of one thing be sure: even if
this ground exists, it’s ugly. It’s a marginal connection at best, especially when dealing with
high-speed logic signals or low level noise-sensitive analog inputs. Never, ever count on it
even when all seems well. Every bit of gear in the lab, probably in the entire building, shares
this ground. When the Xerox machine on the third floor kicks in, the big inductive spike from
the motor starting up will distort the scope signal.
No scope will give decent readings on high-speed digital data unless it is properly grounded.
I can’t count the times technicians have pointed out a clock improperly biased 2 volts above
ground, convinced they found the fault in a particular system, only to be bemused and
embarrassed when a good scope ground showed the signal in its correct zero to five volt
glory. Ground the probe and thus the scope to your target using the little wire that emits from
the end of the probe. As circuits get faster, shorten the wire. The very shortest ground lead
results in the least signal distortion.
Yet most scope probes come with crummy little lead alligator clips on the ground wire that
are impossible to connect to an IC. The frustrated engineer might clip this to a clip lead that
has a decent “grabber” end. Those extra 6–12 inches of ground may very well trash the
display, showing a waveform that is not representative of reality. It’s best to cut the alligator
clip off the probe and solder a micrograbber on in its place.
Figure 1-27: Here we probe a complex non-embedded circuit. Note the
displayed waveform. A person is an antenna that picks up the 60 Hz hum
radiated from the power lines in the walls around us. Some say engineers
are particularly sensitive (though not their spouses).
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Chapter 1
One of the worst mistakes we make is neglecting probes. Crummy probes will turn that
wonderful 1-GHz instrument into junk. After watching us hang expensive probes on the floor,
mixed in with all sorts of other debris, few bosses are willing to fork over the $150 that
Tektronix or Agilent demands. But the $50 alternatives are junk. Buy the best and take good
care of them.
Figure 1-28: Tektronix introduced the 545 scope back in the dark ages;
A half-century later many are still going strong. Replace a tube from
time to time and these might last forever. About the size of a two drawer
file cabinet and weighing almost 100 pounds, they’re still favored by
Luddites and analog designers.
32
CHAPTER
2
Logic Circuits
Jack Ganssle
Coding
The unhappy fact that most microprocessor books start with a chapter on coding and number
systems reflects the general level of confusion on this, the most fundamental of all computer
topics.
Numbers are existential nothings, mere representations of abstract quantitative ideas. We
humans have chosen to measure the universe and itemize our bank accounts, so have developed a number of arbitrary ways to count.
All number systems have a base, the number of unique identifiers combined to form numbers. The most familiar is decimal, base 10, which uses the ten symbols 0 through 9. Binary
is base two and can construct any integer using nothing more than the symbols 0 and 1. Any
number system using any base is possible and in fact much work has been done in higherorder systems like base 64—which obviously must make use of a lot of odd symbols to get
64 unique identifiers. Computers mostly use binary, octal (base 8), and hexadecimal (base 16,
usually referred to as “hex”).
Why binary? Simply because logic circuits are primitive constructs cheaply built in huge
quantities. By restricting the electronics to two values only—on and off—we care little if the
voltage drifts from 2 to 5. It’s possible to build trinary logic, base 3, which uses a 0, 1 and 2.
The output of a device in certain ranges represents each of these quantities. But defining three
bands means something like: 0 to 1 volt is a zero, 2 to 3 volts a 1, and 4 to 5 a 2. By contrast,
binary logic says anything lower than (for TTL logic) 0.8 volts is a zero and anything above 2
a one. That’s easy to make cheaply.
Why hex? Newcomers to hexadecimal find the use of letters baffling. Remember that “A” is
as meaningless as “5”; both simply represent values. Unfortunately “A” viscerally means
something that’s not a number to those of us raised to read.
Hex combines four binary digits into a single number. It’s compact. “8B” is much easier and
less prone to error than “10001011.”
Why octal? Base 8 is an aberration created by early programmers afraid of the implications of
using letters to denote numbers. It’s a grouping of three binary digits to represent the quantities zero through seven. It’s less compact than hex, but was well suited to some early
33